So since all the comments seem to be "Captain America vs. Batman", I'm just going to weigh in.

Given enough time to study his opponent, analyze their strengths and weaknesses, and come up with a plan, there are very few people in the DC or Marvel universes Batman could not defeat. His greatest strengths are not his physical abilities or his gadgets, but his intelligence, creativity and ability to think on his feet, and they've allowed him to defeat opponents who have knocked around superpowered heroes like Superman like play toys.

So in a straight-up fight, Captain America would defeat Batman, but if Batman has time to prepare and plan, he'd defeat Captain America.

I'd say that even in a straight up, impromptu fight, Batman would win. You're right that Batman's best weapon is his intelligence, but I think you're underestimating his physical abilities. In the DC Universe, it's made clear that Batman has achieved human physical perfection; that includes near superhuman strength and reflexes. Partnered with a mastery of more than 7 martial arts, I bet Batman could avoid Captain America long enough to think up a plan, even if Captain had the element of surprise.

That's not at all what I was saying, and I have no idea how you took that from what I said. There are other highly intelligent, highly creative superheroes in both universes (Iron Man is a great example), but the examples you provided all have physical advantages over Batman; Spider-Man has superhuman agility and strength, Iron Man has a suit of advanced power armor, Hulk is a humanoid weapon of mass destruction (and is generally depicted as being a mindless brute full of rage), and Antman......shrinks? (I know nothing about Antman) They all may be as intelligent as Batman, but they have superpowers or advanced technology, and that's where the bulk of their fighting prowess comes from. Batman has none of that; he has to rely entirely on wit to defeat opponents when his physical prowess and gadgets won't do, and he uses that wit to great effect. He goes into battle with contingencies for his contingencies, and that's why he usually comes out on top. It's why his greatest opponents, like Bane, Ra's al-Ghul, even the Joker (in his own demented way), tend to be just as intelligent and creative as him; the enemies who can match his wits are the ones who pose the greatest threat to him, not the ones who can mindlessly pulp him with a single punch.

Batman's the peak of human physiology without any sort of augmentation. Captain America was given a super-soldier serum that makes him stronger, faster and more durable than ordinary humans (though not quite to superhuman levels).

Beyond superhuman. I'd give Captain a 60% chance on beating Batman in hand-to-hand, maybe 70%, but you should never count out Batman, and either way neither of them would fight the other as they'd make one of the best Superhero tag teams ever.